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## Archive of Issues

Russia Izhevsk
Year
2012
Issue
2
Pages
106-113
 Section Mechanics Title On the application of random searching for the hard particles packing problem for composite solid propellant structure modeling Author(-s) Bolkisev A.A.a Affiliations Institute of Mechanics, Ural Branch of the Russian Academy of Sciencesa Abstract The paper presents a problem statement for random hard particles packing as minimization of an objective function that is the measure of overlapping of $\mathbb{R}^3$ subdomains representing particles and forbidden zones, with desired pack characteristics being accounted for by an additional summand in the objective function. A new algorithm based on the random search approach is proposed; it assesses a new particles configuration after each movement, and particles grow from an initial to full size as overlaps being removed. This algorithm is matched with the viscous suspension algorithm for the case of packing equal-sized spheres in a periodic cube. For packing fractions $\varphi<0,55$ the random search algorithm yields packs with fewer and smaller particle clusters than the viscous suspension one, in denser packs differences are insignificant. An example of creating a pack with the feature that particles are shifted closely to the solid boundary is shown as well. Keywords hard spheres, hard particles, packing, random searching, composite solid propellant structure UDC 519.688 MSC 49K45, 05B40 DOI 10.20537/vm120210 Received 16 March 2012 Language Russian Citation Bolkisev A.A. On the application of random searching for the hard particles packing problem for composite solid propellant structure modeling, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 2, pp. 106-113. References Rashkovskii S.A. Structure of heterogeneous condensed mixtures, Combustion, Explosion, and Shock Waves, 1999, vol. 35, no. 5, pp. 65-74. Lubachevsky B.D., Stillinger F.H. Geometric properties of random disk packings, Journal of Statistical Physics, 1990, vol. 60, no. 5/6, pp. 561-583. Knott G.M., Jackson T.L., Buckmaster J. Random packing of heterogeneous propellants, AIAA Journal, 2001, vol. 39, no. 4, pp. 678-686. Davis I.L., Carter R.G. Random particle packing by reduced dimensions algorithms, Journal of Applied Physics, 1990, vol. 67, no. 2, pp. 1022-1029. Tanner M.W. Multidimensional modeling of solid propellant burning rates and aluminum agglomeration and one-dimensional Modeling of RDX/GAP and AP/HTPB, Ph. D. Diss., Brigham Young University, 2008, 244 p. Webb M.D., Davis I.L. Random particle packing with large particle size variations using reduced-dimension algorithms, Powder Technology, 2006, vol. 167, no. 1, pp. 10-19. Shi Y., Zhang Y. Simulation of random packing of spherical particles with different size distributions, Applied Physics A: Materials Science & Processing, 2008, vol. 92, no. 3, pp. 621-626. O'Hern C.S., Langer S.A., Liu A.J., Nagel S.R. Random packings of frictionless particles, Physical Review Letters, 2002, vol. 88, no. 7, pp. 1-4. Jia X., Williams R.A. A packing algorithm for particles of arbitrary shapes, Powder Technology, 2001, no. 120, pp. 175-186. Lipanov A.M. Fiziko-khimicheskaya i matematicheskaya modeli goreniya smesevykh tverdykh topliv: preprint (Physico-chemical and mathematical models of burning of mix solid propellants: preprint), Izhevsk: Institute of Applied Mechanics, Ural Branch of RAS, 2007, 112 p. Rastrigin L.A. Teoriya i primenenie sluchainogo poiska (Theory and applications of the random search), Riga: Zinatne, 1969, 307 p. Raschdorf S., Kolonko M. A comparison of data structures for the simulation of polydisperse particle packings, International Journal for Numerical Methods in Engineering, 2011, vol. 85, no. 5, pp. 625-639. Kamien R.D., Liu A.J. Why is random close packing reproducible? Physical Review Letters, 2007, vol. 99, no. 15, pp. 1-4. Torquato S., Truskett T.M., Debenedetti P.G. Is random close packing of spheres well defined? Physical Review Letters, 2000, vol. 84, no. 10, pp. 2064-2067. Rashkovskii S.A. Statistical modeling of burning processes of heterogeneous condensed mixtures, Dr. Sci. (Phys.–Math.) Dissertation, Moscow, 2004, 428 p. Full text